Posted by **Amy** on Sunday, October 16, 2011 at 12:50am.

Prove that you have constructed point C on segment EF such that angle ACE is congruent to angle BCF. (Points A and B are on the same side of segment EF, but have different distances to the segment.)

I am not sure if I am on the right track but this is how I have tried prove it: I have proven a new angle, angle ICF, is congruent to angle ACE by the Vertical Angle Theorem (after introducing line AC and point I at the intersect of line AC and line BD (which is perpendicular to segment EF)). I have introduced point J on line BD such that JD=ID and proved triangle CJD is congruent to triangle CID by SAS (CD=CD by Reflexive Property, angle JDC is congruent to angle IDC because line BD is perpendicular to segment EF (which contains point C) therefore angles JDC and IDC are right angles and all right angles are congruent, and I had introduced point J so that JD=ID). At the moment I cannot see how I would prove point J is point B, so I am not sure if the above reasoning is in the right direction.

Thank you for your help!

## Answer this Question

## Related Questions

- geometry - given: segment AB is paralell to segment DC; segment AB is congruent ...
- Geometry - According to the given information, segment AB is parallel to segment...
- Geometry - Given: angle BAC is congruent to angle ACD, segment BD bisects ...
- Geometry - Yes, I'm this desperate. I just have problems with coming up with the...
- Geometry - Given: Segment CE bisects <BCD; <A is congruent to <B Prove...
- geometry - I need to figure out this proof, the figure is two triangles forming ...
- Geometry - Given: segment AE and segment CD are lines. Prove: angle ABD is ...
- Geometry - Given: segment AE and segment CD are lines. Prove: angle ABD is ...
- Geometry HELPP - I need a conclusion and reason for the following statements. 1...
- Geometry - Given: segment AB is congruent to segment BC; angle 1 is congruent to...